Background

Nonlinear functions can serve as a powerful tool for creating sounds in
musical synthesizers.
Among the best known wave shapers are the overdrive in
one form or the other (soft of hard clipping, used by myriads of
guitarists,
and used as a triangle-to-sine shaper and saw-to-pulse shaper in
synthesizers),
and the full wave rectifier (used as
saw-to-triangle
shaper in synthesizers).
These wave shapers can be used in a static way (careful adjustment
for low distortion in triangle-to-sine conversion), but the real fun
starts
when parameters are changed dynamically. Pulse Width Modulation means
adding
a variable offset voltage to the input of a very "steep"
hard limiter (a.k.a. comparator), for instance. And a guitarist can get
a variety of sounds out of his overdriven tube amplifier by just
altering
the input gain.
There is one type of waveshapers that has a kind of "mystery" status:
The Serge Wave Multipliers,
especially its "Middle Section". Obviously related to
the full wave rectifier type, this performs a "folding back" of peaks
that
exceed a certain limit. Unlike a simple full wave rectifier, this
happens
not once, but several times as the input signal increases. The voltage
transfer function must be "non-monotonous", i.e. it has several "peaks"
and "valleys". The sonical effect of an input signal with decaying
amplitude
can be similar to FM at times.

How to emulate a Wave Multiplier ?

It's quite easy to produce a similar effect with the Interpolating
Scanner I have introduced a few years ago, by simply setting the
breakpoints
to min - max - min - max, and so on. But building a Scanner to emulate
a partially periodic voltage transfer function means breaking a fly on
a wheel. Especially when the original Serge circuit is so simple - and
so brilliant. I am not entitled to disclose the original, and I will
make
no attempt to publish a "slightly modified" version.
But I have made some experiments with other "simple" circuits, and
I finally found a circuit for a wave folder core that only needs 3
opamps
- that's a "single chip wavefolder" (;->).
I don't claim it emulates the Serge perfectly (I know it does not),
but from my first experiments I've seen that it opens a door to a
multitude
of different possible transfer functions. I have yet to explore how
much
variance of the transfer function really makes sense, because you can
already
get so many different output wave shapes by just changing the input
level
and input offset voltage.

The following is my first version of the wave folder: Shaper
A (PDF, 35kB)
A string of diodes is driven with the amplified and level shifted input
signal. After each diode there is a "tap" with a resistor that will
contribute
positive or negative to the output of a two-opamp subtracting
amplifier.
There are two virtual GND nodes for these summing and subtracting
operation.
By feeding these virtual GND nodes alternately from the taps of the
diode
string, you can have the output voltage increased when one diode drop
voltage
is reached, and have the output voltage decreased again when the next
diode
in row starts conducting. The number of valleys and peaks is only
determined
by the length of the diode string, and not by the number of opamps. It
turned out that choosing equal resistor values results in an almost
regular
pattern of the voltage transfer function. It's not perfect - the slight
unsymmetry is clearly visible in the simulation
plot.

Variations

It's probably possible to adjust the resistor values to get a better
fit.
But the opposite is more rewarding: change resistor values to get
different
transfer functions which are farther from the Serge wavefolder, but
still
have a smooth character to scan thru various harmonics.
Here is an example for a new wave shaper that doesn't have much in
common with Serge anymore: Shaper B
(PDF,
74kB)
With a single 10k linear potentiometer you can get a variety of
different
nonlinear transfer functions. They all share the "smoothness" of the
courves,
and they all have that "FM kind" character, but the degree of "metal"
in
the sound changes with different potentiometer settings.

Applications

I have built Shaper A and Shaper B on breadboard, and I have tested it
with unfiltered sine waves from synthesizers, and with a guitar sound
from
a Yamaha VL7.
The synthesizer waveforms definitely need a VCA at the input of the
Shapers. An OTA to the summing node of the input amplifier will do, but
I have made tests with the VCO and VCA of a modular system.
The VL7 guitar does not need any VCA in front of the Shaper. (And
neither
does a real guitar, I guess). So the circuit makes sense as a novel
kind
of guitar stomp box without many additions (a high impedance input amp,
input and output level potentiometers, bypass switch ...). And it make
sense as a standalone Module with one VCA included in a Modular
Synthesizer.
Juergen
Haible